Nice one pal, great that you have it a go in the cold showers. I have to little ones so getting up and ready early doors helps juggle the circus!! I felt that the cold showers help knock out any aches and pain I have when waking up also and make me less hungry throughout the morning - which after Xmas was worth it alone. The benefits to immune of course can't been seen or felt at a glance.
My routine is 3 mins countdown, first minute to rinse off and acclimatise, sud up for another minute or so then the last minute rinse of saying the Lord's prayer and for me I'm almost embassed to say that I can drift off when praying into other thoughts. Yet when said in the cold shower, because the cold is all consuming each and every word is the sole focus of my mind which I really like.
How long do you manage with the breathing?